!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CHANCE News 3.03
(13 February to 5 March 1994)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Prepared by J. Laurie Snell as part of the
CHANCE Course Project supported by the
National Science Foundation and the
New England Consortium for Undergraduate
Science Education.
Please send suggestions to:
dart.chance@dartmouth.edu
Current and previous issues of CHANCE
News can be found on our chance gopher.
Just point your gopher to:
chance.dartmouth.edu
====================================
Public ignorance of the laws of evidence and of
statistics can hardly be exaggerated.
G.B.S
====================================

Paulos turns his popular writing skills to the subject
of the public's understanding of statistical issues in
medicine. He begins by citing three general problems:
(a) inability to confront numbers associated
with health hazards objectively
(b) ignorance about the oddities of
statistical analysis
(c) lack of factual knowledge of how
the statistics were obtained.
He then gives numerous examples to illustrate each of
these problems. To illustrate the problem of being
objective he describes the hysteria over the report on
television of the man who claimed that there was a
causal connection between his wife's frequent use of a
cellular phone and her subsequent brain cancer.
Misunderstanding of statistical ideas are illustrated in
terms of examples such as Simpson's paradox. For
instance, two studies, both found that a higher percent
of minority group A were improved by a drug than was the
case for minority B. But when the data for the two tests
were combined, a higher percent of group B improved than
group A.
Lack of information is illustrated by the often quoted
statistic that condoms fail 10 percent of the time,
which apparently originated from asking couples whether
condoms ever failed them in birth control. It was then
applied to such things as protection against AIDS.
Another example is the famous 10 percent homosexual
estimate. Paulos remarks that we seem to be given
numbers like 10 that we feel more comfortable with than
numbers like 11 or 12.
You'll find a wealth of examples here, some old
favorites, some new favorites and some that you probably
haven't heard of at all - but all written in the lively
Paulos style.
<<<========<<

An argument *against* gun control in a liberal magazine!
Polsby challenges a number of widely held beliefs,
claiming that "guns don't increase national rates of
crime and violence---but the continued proliferation of
gun control laws almost certainly does."
He says most major newspapers go along with the article
by Arthur Kellerman and several associates in the 7
October 1993 New England Journal of Medicine, which
intended to discredit the idea that having a gun is a
useful means of self-protection.(See Chance news 2.17
and 3.02) Describing Kellerman's study, Polsby
challenges Kellerman's conclusion that owning a handgun
increases a person's risk of being murdered, claiming
that the study may in fact indicate the opposite causal
arrow; that the fear of being murdered makes people arm
themselves.
Polsby goes on to cite several examples which, he says.
contradict notions commonly held by gun-control
advocates: Switzerland, New Zealand and Israel have
about the same guns-per-civilian-household rate as the
US, yet lower rates of crime and violence; Mexico and
South Africa have gun control, but murder rates twice as
high as here.
Besides citing statistics, Polsby also explains why he
believes that gun control laws cannot bring about what
they are intended to; those who really must have guns
for their work, including some criminals, will continue
to get them no matter what the costs.
The climax of the article is his assertion that "the
root cause of crime is that for certain people predation
is a rational occupational choice", and he suggests
progressive policies to remedy the social situations
that make this true.
This is an article that is really full of statistical
assertions, but without any hard numbers. For instance
"Mexico, which has tighter gun control laws than the US,
has a much higher murder rate."
DISCUSSION QUESTION: In reply to criticism of their
article, Kellerman and his colleagues remark that their
study is similar to the initial studies that led to the
verification of a causal connection between smoking and
lung cancer. Polsky, says that the difference here is
that no-one thought that lung cancer could possibly
cause smoking but with the gun issue both arrows are
perfectly possible. What kind of further studies are
necessary to clarify this point?
<<<========<<

An in-depth story of the study to test the drug
fialuridine (FIAU) as a cure for hepatitis B that went
wrong and was stopped after the death of several of the
subjects. (See Chance News 2.15 for more details of
this study)
<<<========<<

The story of the life and work of Simon LeVay since he
discovered a minute but measurable difference in the
size of a part of the brain of homosexual and
heterosexual men.
LeVay's instant fame and involvement with the gay
community led him to give up his research career and
help found an extension school for adults taught by
lesbians and homosexuals, teaching a wide range of
courses involving sexual orientation in law, science,
literature, the arts etc.
The article also reviews other studies that suggest that
sex preference is a genetic trait. (See Chance News 2.13
and 2.14).
<<<========<<

Discusses ethical questions related to conducting trials
of experimental AIDS vaccines in a way that respects the
rights of research subjects.
One concern is that the urgency surrounding the epidemic
may lead to premature human testing of new treatments.
There have also been reports that treatments which show
promise in the lab can be less effective in the real
world, apparently because of differences among strains
of the virus.
Vaccines currently under development to reduce
vulnerability to HIV infection are not expected to be
more than 50-60% effective, making it all the more
important that people understand and weigh the risks and
benefits of vaccination.
Finally, it is noted that some high risk groups such as
IV drug users, young gay males, and persons of color
tend to have less access to medical care, and may be
difficult to recruit for testing.
<<<========<<

This review was motivated by a recent study reported in
the Journal of the National Cancer Institute and
characterized in an accompanying editorial as showing
"conclusively that use of permanent hair dyes does not
increase risk of cancer mortality."
In 1982 about 500,000 women age 30 and over, enrolled in
a cancer prevention study conducted by the American
Cancer Society. Among the information obtained was
their use of hair dyes, including the color, type and
length of use. Researchers then measured death rates
from cancer among these women through 1989. After
controlling for smoking and other risk factors for
cancer, they found that hair dye showed no relation to
cancer deaths.
As in previous studies, there was a suggestion that long
use of dark dyes, especially black dye, could increase
the risk of non-Hodgkin's lymphoma and multiple myeloma,
two potentially fatal cancers. A similar study, the
Harvard nurses study, has also not found an overall
increase in cancer risk among users of hair dyes, though
this study is still in progress.
Concern has been expressed about the use of hair dye
based on the work of Bruce Ames at Berkeley who pointed
out that the colorants are derived from coal tars, known
to be carcinogenic. In addition, animal tests using very
high doses of dyes did indicate that permanent hair dyes
might be carcinogenic. I think coal tars are no longer
used.
Previous studies had indicated some risk, but it is
claimed that this was not a consistent finding and the
authors did not control for smoking and other known risk
factors.
<<<========<<

Epstein is chairman of the Cancer Prevention Coalition
and writes that the recent study of the American Cancer
Society showing little danger in using hair dyes is
"seriously flawed in design and interpretation."
One concern is that the study was based on women whose
average age was only 56 when they were first enrolled in
the study, and only 63 when they were no longer being
followed. Epstein observes that the really high rates
for the cancers of concern occur after age 63 and that
most of these would be missed by the study.
He also feels that the study did not control for some
important risk factors such as duration of oral
contraceptive use and a history of mammogram tests. In
addition, those who started using hair dye after the
beginning of the study were counted as non-users.
He claims that "a well designed study in Nebraska found
that hair dye use would account for about 20 percent of
all non-Hodgkin's lymphoma deaths in women". He
considers the accompanying editorial even more
recklessly misleading than the study and recommends that
women switch to non carcinogenic organic hair dyes.
<<<========<<

The authors of the hair dye study reply to the above
letter from Epstein. They disagree with Epstein's
concern about their not controlling for mammography use,
saying that there is no evidence that women who use hair
dye have mammography more or less than women who use no
dye. They remark that they did recommend that
carcinogens be removed from hair dye and that women
avoid long-term use of black dye.
<<<========<<

This is an account of the Nebraska study mentioned by
Epstein in his letter. It was also carried out by
scientists at the National Cancer Institute. Researchers
conducted a phone survey of 583 blood-related cancer
cases and 1,432 controls, all white men and women living
in 66 eastern Nebraska counties. The study was published
in the American Journal of Public Health.
Among women, use of all hair coloring products was
associated with non-Hodgkin's lymphoma, Hodgkin's
disease, and multiple myeloma. Permanent hair coloring
methods caused more risk then non-permanent coloring.
The risk to men who used hair coloring was higher but
not significantly so.
<<<========<<

This is a report issued by the Cosmetic, Toiletry, and
Fragrance Association which quotes a number of leading
epidemiologists saying that the Nebraska study made
claims that were not at all supported by the data.
References are given to other studies that support the
fact that hair dyes do not cause cancer.
PROJECT SUGGESTION: Look up the original articles on
cancer and hair dye and determine your own opinion about the
present state of this argument.
<<<========<<

Part B. What are the results and will they help me in
caring for my patients?
Journal of American Medical Association,
2 Mar 1994, Pg. 703
Roman Jaeschke and others

The authors start with a clinical scenario that leads
you (the doctor) to suspect that your patient has a
pulmonary embolus (PE) (an obstruction in the lungs).
You request a ventilation-perfusion scan (V/Q
scan)(seems to measure rate of flow through the lungs),
and the result, reported to the nurse over the
telephone, is "intermediate probability for PE". Should
you proceed to treat the patient as if she has PE?
In part A the authors show how you can find in the
literature studies that tell you the meaning and the
basis for the "intermediate probability". In particular,
you find a study in which 731 patients suspected of
having PE were given V/Q tests with the results reported
as high probability, intermediate probability, low
probability, or normal for having PE. Then by an
independent, essentially foolproof, test determined if
the patient did have PE.
The results of this experiment were: For those reported
as high probability, 102 had PE and 14 did not, for
intermediate probability 105 had PE and 217 did not, for
low probability 39 had PE and 273 did not and for near
normal 5 had PE and 126 did not.
Part B shows you how to combine results from this study
with your prior probability for the patient having PE to
obtain a posterior probability. To emphasize the role of
the prior probability two patients are considered, one
young and one old, with comparable symptoms.
The authors also discuss the method of sensitivity and
specificity but suggest that this older method is a less
useful approach and they mention it only because it is
still used in the literature.
DISCUSSION QUESTION: Before getting the results of the V/Q
scan, on the basis of the patients other symptoms, the
doctor assigned a 40 percent chance that the patient had PE.
What probability should the doctor assign after the test and
the result "intermediate probability for PE"?
<<<========<<

A study designed to see if the drug AZT would help
prevent the HIV virus from being passed on to the child
of an HIV positive pregnant women, has been stopped
early because of its unexpected success.
The study involved 477 women in 50 medical centers in
the United States and 9 in France who had tested
positive for the HIV virus but still have more than a
200 CD-4 count. The women were enrolled between the 14th
and 34rd week of their pregnancy and agreed to receive
either AZT or placebo pills during pregnancy and labor.
The 477 women gave birth to 421 babies. Of the 364
babies for whom at least one culture test was available,
53 were HIV positive. 40 of these were from mothers who
had placebo while 13 were from mothers who had taken AZT
pills. It has been estimated that about 25% of the time
a child of a mother infected with HIV will be infected,
so that the 26% in the placebo group reassured the
investigators. So far, no added birth defects have been
attributed to the AZT.
The results of this study provide a host of problems
ethical and otherwise. The transmission of AIDS through
childbirth is a major problem in the developing
countries and those involved will not be able to afford
the AZT. The results argue for more aggressive testing
of pregnant women which conflicts with privacy rights
etc. Needless to say, panels have been established to
study these problems.
DISCUSSION QUESTION: Given the mixed results on AZT in
previous studies, do you think the researchers were
justified in stopping the study before they had time to
look for side effects? Do you think that there should
be mandatory testing for the HIV virus of pregnant
women.
<<<========<<

San Francisco is one of the very few success stories in
attempts to stop the spread of AIDS. The San Francisco
Department of Public Health reported that 3,326 people
developed AIDS in the peak year of 1992. The number
dropped to 1,507 in 1993. It is expected that the number
in the coming years will continue to decline, but
slowly.
This dramatic decrease is attributed to the extensive
education campaigning carried out among the groups at
highest risk for AIDS: gay and bisexual men and
intravenous drug users.
Experts say that for the immediate future, educational
programs hold out more hope than vaccines in stopping
the spread of AIDS.
<<<========<<

>>>>>==========>>
Obstacle-Strewn Road to Rethinking the Numbers on AIDS.
The New York Times, 1 March 1994, C3
Lawrence K. Altman
The usual estimate for the number of people with the HIV
virus in the United States is one million, which is
based upon the 1989 estimate of the Centers for Disease
Control that the number is between 800,000 and
1,200,000.
The CDC plans to make a new estimate in July, and, in
preparation, the agency invited independent experts to
meet last week to report and review relevant data.
Although some of the estimates went as high as a
million, most ranged from 600,000 to 800,000.
The article discusses the many difficulties in making
reliable estimates for the number of people with AIDS:
the social stigma makes people afraid to report the
disease. In addition, where it occurs is constantly
shifting. For example, the biggest group has been white
gay men, but the number in the group is thought to be
declining while the number of black women in the South
is increasing. Figures are not kept on a yearly basis
and so it is hard to estimate trends. Plans are being
made to remedy this by making spot surveys on an annual
basis.
Government officials point out that an estimate that the
number of HIV people is decreasing could have serious
consequences in government policy for providing money
for the fight against AIDS.
This will leave the CDC with the problem that "letting
the data speak for itself" may not be the best way to
fight the disease.
DISCUSSION QUESTION: Should the CDC let the data speak
for itself?
<<<========<<

A study reported in the current Journal of the American
Statistical Association shows that inner-city alcoholics
have a surprisingly high rate of HIV infection.
Researchers reviewed the records of 639 men and 221
women who underwent treatment for alcoholism at five
city-operated neighborhood health centers in San
Francisco and who identified themselves as heterosexual.
Previous studies would have suggested that about 1/2 a
percent of heterosexuals with a similar background
should be HIV infected. In this group they found about 5
percent.
Among the group studied, about 1/4 were homeless and 3/4
were unemployed. Still, of the 139 who said they worked
full time and have a place to live, about 4 percent were
HIV positive.
Of course, the obvious explanation would be that the
use of alcohol leads to unprotected sex.
DISCUSSION QUESTION: What are other explanations for
the difference in incidence of HIV infection in the
group studied?
<<<========<<

The current issue of Lancet has an article reporting on
a Dutch study that showed that women who had been taking
tamoxifen for more than two years were more than twice
as likely to develop endometrial cancer than those not
taking the drug. The risk increased with time and the
amount taken. Women taking the drug for more than five
years were three times more likely to have endometrial
cancer.
The risk for cancer has been known for some time but the
benefits of tamoxifen for women already diagnosed as
having breast cancer is felt to outweigh the increased
risk for endometrial cancer.
Studies to test the use of tamoxifen to prevent breast
cancer for those at high risk are just starting in
England and have been going on for some time in the
United States and in other countries as part of a large
international study.
A member of the research team for this study is quoted
as saying: "It is debatable whether the use of a medical
intervention can be justified when it prevents breast
cancer in some women at the cost of inducing endometrial
cancer in others."
The chairman of the international study stated that they
were aware of the Dutch study and, in fact, the risks
they found were lower than those that they had assumed
in planning the study. He commented:
We have been working on the possibility of a
threefold risk. This level means that over the
five years the women in the trial are taking
tamoxifen, their risk of developing endometrial
cancer rises from 2 per 1,000 women to 5
per 1,000.
But we do not see it as a reason for denying
the option of taking part in the trial to the
women at increased risk of breast cancer.
They are being informed of the potential risks
as well as the potential benefits."
An article on this topic in 18 February issue of Science
comments that some changes have been made in the US
study in the informed consent form on the basis of these
news studies.
DISCUSSION QUESTION: Is it fair to say that the
tamoxifen study "prevents breast cancer in some women at
the cost of inducing endometrial cancer in others"?
<<<========<<

The current issue of the New England Journal of Medicine
gives the results of a study that surveyed 371 patients
over one year at a geriatrics clinic at the medical
center. Initially 41 percent said they would like to
have CPR if their hearts stopped while they were being
treated for an acute illness. (CPR is used to shock the
heart back to life after cardiac arrest.) But when they
were told that their chances of surviving were only 10
to 17 percent, the percentage who would like to have it
dropped to 22%.
The article suggests that making sure patients
understand the chances for success might cut down health
costs, but another article in the same issue points out
that this is not so obvious.
<<<========<<

A study reported in the current New England Journal of
Medicine indicates the decision of Insurance companies
to pay for the care of patients seems "capricious and
arbitrary".
The authors, Dr. William P. Peters and Dr. Mark C.
Rogers of Duke University, stated that about a 1/4 of
insurance companies refused to pay for women to have
bone marrow transplants and high-dose chemotherapy as
part of a federally sponsored clinical trial. For two
very similar patients, one may be supported and the
other not.
Of the 533 women who wanted to enter the study of bone
marrow transplants and high-dose chemotherapy for
advanced breast cancer, 411 got assurances that their
health insurance companies would pay. Of the 121 who
were told they would be denied payment, 62 had the
transplant anyway. 39 later managed to persuade their
insurance companies to reverse the decision not to pay,
and about half of them did this after getting a lawyer
and threatening to sue.
Insurance companies point out since the subjects are
participating in a trial the treatment is clearly
experimental and therefore they really don't have to pay
for the treatment. A researcher countered by saying that
if a subject received placebo they would receive payment
for the treatment.
DISCUSSION QUESTION: Do you think that it is reasonable
that drug companies not pay for treatments that are
considered experimental? If so, how do you think the
insurance companies should decide if a treatment is
experimental?
<<<========<<

The College Board is making the first major revision in
its S.A.T. exams in 20 years. The revised verbal section
puts more emphasis on ability to analyze passages of
text, and the math section has students solve problems
rather than pick multiple-choice answers. And students
may use calculators.
All this has been a boon to the coaching companies who
report that business is booming. To avoid making
coaching available only to the rich, schools are
offering free coaching. There is, of course, the usual
argument about how much coaching can help. The ETS
people say only about 30 to 50 points beyond the normal
25 point gain between the preliminary and actual tests.
It is claimed that recent audits by two independent
accounting firms concluded that students who took a
preparation course typically increased their scores by
up to 125 points. It would be interesting to see how
these audits were carried out.
The executive director of the National Center for Fair
and Open Testing comments that the changes are only
cosmetic and feels that, despite the efforts of the ETS
to avoid bias, the test is still unfair to minorities
who cannot afford to learn the tricks from the coaching
services.
DISCUSSION QUESTION. Why is it so difficult to
determine how much coaching improves students with SAT
scores? What kind of test would you design to settle
this matter once and for all?
<<<========<<

The author tells of his experience with the following
activity. Students were told that was their job to
design and carry out an experiment which would
investigate the operation of short term (working)
memory.
The students decided to work in pairs, one person
constructing a list of 12 words which were read to the
partner and the partner then asked to recall as many as
possible. A discussion moderated by the instructor led
to a number of conditions to be met on the choice of
words, how they should be read, time between answering,
etc.
In the first experiment the words were unrelated, in the
second they were related, and in the third they were
unrelated and, between reading and recalling, the
student who is trying to recall the words was given the
exercise of counting backwards in 7's from 256.
The students plotted the outcomes in terms of the
proportion who remembered questions in the various
positions in the list. It was observed that the
beginning and the end of the list are remembered best,
that the counting exercise makes it harder, etc. The aim
is to show that interesting things can be learned by
very simple statistical experiments.
<<<========<<

The author shows the students a number of quotations
from the newspapers that describe a "rule of thumb". For
example, from the Guardian: "As a rough rule of thumb,
withdrawal symptoms are thought to last a month for
every year on tranquilizers."
The author describes an activity designed to have the
students develop their own "rule of thumb". To do this,
students are asked to pick 6 cities at random from a
list of the 42 cities in England. For each of the 15
possible pairs of cities in their group the students are
asked to find two measurements: (a) how far apart they
are "as the crow flies" and (b) how far apart by driving
on reasonable roads. They then are asked to make a
scatter plot, fit a line by eye, and determine the "rule
of thumb" from the equation of this line. Students can
check the rule and determine confidence intervals etc.
<<<========<<

If you are trying to determine basketball shots or the
up and down of a stock that exhibits streaky behavior,
you are apt to want to find the distribution for the
number of runs. If you condition on the number of
successes, there are simple combinatorial expressions
for the probabilities for r runs. If you do not want to
condition this way, there do not seem to be reasonable
expressions for the probability of r runs.
The author observes that these probabilities can be
computed recursively very simply. This is described in
terms of Markov Chains, but no knowledge of Markov
Chains is necessary to understand the calculation.
Some interesting properties of these probabilities are
discussed and proven. For example, the probability that
the number of runs is odd is independent of the number
of trials, provided there are 2 or more trials.
<<<========<<

This is a brief discussion from a statistician working
at Lilly on how trials are carried out. The author
illustrates the procedure in terms of a trial comparing
four groups of patients being treated for stomach
ulcers: group 1 receiving placebo, group 2, active drug
at dose d twice a day, group 3, active drug at dose 2d
once per day, and group 4, active drug at dose 2d twice
per day.
The use of logistic regression illustrates both the
effectiveness of the four different treatment procedures
and risk factors such as drinking, age etc.
DISCUSSION QUESTION. In the log regression analysis, the
parameter for the drinking variable (yes or no)
translates to an odds ratio of about 2 to 1. The authors
concludes from this that "the odds of being cured if you
are a drinker vs. not being a drinker) are about 1:2.
Why can they say this?
Karl Pearson and R.A. Fisher on statistical tests:
A 1935 Exchange from Nature
American Statistician, Feb 1994, Page 2
Henry F. Inman
The meaning of statistical tests is still a hot issue on
statistical discussion groups and it is interesting to see
what the masters argued about.
This exchange of letters was prompted by a letter from a
practicing statistician Buchanan-Wollaston criticizing the
work of the British school. He wrote "The fact that British
methods 'work' is due to the prevalence in Nature of
distributions similar to the Gaussian rather than to any
peculiar virtue of the methods themselves.
Pearson replies that his chi-squared test has nothing to do
with any normal assumption and is just a way to measure the
goodness of fit of the data by a particular distribution.
"If Continental statisticians in the bulk do indeed hold the
views of Mr. Buchanan-Wollaston, it can only be that they
have not really studied and grasped the fundamental
literature of the subject."
Fisher writes that Pearson's own writings show that he
certainly does use the chi-squared to test hypotheses. He
agrees with Buchanan-Wollaston that the chi-squared test is
relevant for rejecting a hypothesis but not for acceptance.
Fisher writes: "'errors of the second kind' are committed
only by those who misunderstand the nature and application
of tests of significance."
Pearson replies ridiculing the idea that you can test
whether a hypothesis is true but not if a hypothesis is
false. He concludes his second letter with "The 'laws of
Nature' are only constructs of our minds, none of them can
be asserted to be true or to be false, they are good in so
far as they give good fits to our observations of Nature."
I have given quotes out of context just to whet your
appetites to real the letters.
<<<========<<